The acceleration due to gravity about the earth's surface would be half of its value on the surface of the earth at an altitude of ……… $mile$. ($R = 4000$ mile)

Weightlessness experienced while orbiting the earth in space-ship, is the result of

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)

A body weights $49\,N$ on a spring balance at the north pole. ….. $N$ will be its weight recorded on the same weighing machine, if it is shifted to the equator?

(Use $g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}$ and radius of earth, $R =6400\, km .]$

Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then